Ballooning instabilities on a magnetic separatrix

The stability of plasmas to localized ballooning modes on a magnetic separatrix (such as occurs with divertor tokamak configurations) is considered. The ideal MHD ballooning eigenmode equation is first derived for a general Clebsch representation and then specialized to particular divertor magnetic flux surface representations. A combination of analytic and numerical calculations is used to show that ballooning instability occurs for dp/dr > (B2/2μ0)R0/l/sub c/2 where the connection length l/sub c/ is found to be approximately the distance between X-points on the separatrix. The possible role of these instabilities in tokamak H-mode edge fluctuations (H/sub α/ spikes, quasi-coherent fluctuations) is also discussed